- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 16:49:54
3
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=JEMS&vol=2&iss=1&update_since=2024-03-29
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
2
2000
1
Stable ergodicity and julienne quasi-conformality
Charles
Pugh
University of California, BERKELEY, UNITED STATES
Michael
Shub
University of Toronto, TORONTO, ONTARIO, CANADA
In this paper we dramatically expand the domain of known stably ergodic, partially hyperbolic dynamical systems. For example, all partially hyperbolic affine diffeomorphisms of compact homogeneous spaces which have the accessibility property are stably ergodic. Our main tools are the new concepts - julienne density point and julienne quasi-conformality of the stable and unstable holonomy maps. Julienne quasi-conformal holonomy maps preserve all julienne density points.
Dynamical systems and ergodic theory
General
1
52
10.1007/s100970050013
http://www.ems-ph.org/doi/10.1007/s100970050013
Almost invariant submanifolds for compact group actions
Alan
Weinstein
University of California, BERKELEY, UNITED STATES
Abstract. We define a C1 distance between submanifolds of a riemannian manifold M and show that, if a compact submanifold N is not moved too much under the isometric action of a compact group G, there is a G-invariant submanifold C1-close to N. The proof involves a procedure of averaging nearby submanifolds of riemannian manifolds in a symmetric way. The procedure combines averaging techniques of Cartan, Grove/Karcher, and de la Harpe/Karoubi with Whitney's idea of realizing submanifolds as zeros of sections of extended normal bundles.
Differential geometry
Manifolds and cell complexes
General
53
86
10.1007/s100970050014
http://www.ems-ph.org/doi/10.1007/s100970050014
Erratum: J. Eur. Math. Soc. 1, 237-311 (1999)
General
87
91
10.1007/s100970050015
http://www.ems-ph.org/doi/10.1007/s100970050015